# Uniform-in-Phase-Space Data Selection with Iterative Normalizing Flows

arXiv: https://arxiv.org/abs/2112.15446 · HTML: https://mlsanity.com/paper/2112.15446/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 78 references that are in the map.
- First posted on arXiv 28 Dec 2021.

## Builds on (most cited first, 15 of 15)

- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Nonparametric Density Estimation for High-Dimensional Data - Algorithms and Applications](https://mlsanity.com/paper/1904.00176/) (2019)
- [Adversarial sampling of unknown and high-dimensional conditional distributions](https://mlsanity.com/paper/2111.05962/) (2021)
- [Visualization-Aware Sampling for Very Large Databases](https://mlsanity.com/paper/1510.03921/) (2015)
- [Void-and-Cluster Sampling of Large Scattered Data and Trajectories](https://mlsanity.com/paper/1907.05073/) (2019)
- [Multivariate Pointwise Information-Driven Data Sampling and Visualization](https://mlsanity.com/paper/1907.11762/) (2019)
- [Impact of Data Pruning on Machine Learning Algorithm Performance](https://mlsanity.com/paper/1901.10539/) (2019)
- [It was the training data pruning too!](https://mlsanity.com/paper/1803.04579/) (2018)

## Built on by (most cited first, 3 of 3)

- [PINN surrogate of Li-ion battery models for parameter inference. Part I: Implementation and multi-fidelity hierarchies for the single-particle model](https://mlsanity.com/paper/2312.17329/) (2023)
- [A Priori Uncertainty Quantification of Reacting Turbulence Closure Models using Bayesian Neural Networks](https://mlsanity.com/paper/2402.18729/) (2024)
- [Intelligent Sampling of Extreme-Scale Turbulence Datasets for Accurate and Efficient Spatiotemporal Model Training](https://mlsanity.com/paper/2508.03872/) (2025)

## Abstract (arXiv)

Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that is routinely generated. In applications that are constrained by memory and computational intensity, excessively large datasets may hinder scientific discovery, making data reduction a critical component of data-driven methods. Datasets are growing in two directions: the number of data points and their dimensionality. Whereas dimension reduction typically aims at describing each data sample on lower-dimensional space, the focus here is on reducing the number of data points. A strategy is proposed to select data points such that they uniformly span the phase-space of the data. The algorithm proposed relies on estimating the probability map of the data and using it to construct an acceptance probability. An iterative method is used to accurately estimate the probability of the rare data points when only a small subset of the dataset is used to construct the probability map. Instead of binning the phase-space to estimate the probability map, its functional form is approximated with a normalizing flow. Therefore, the method naturally extends to high-dimensional datasets. The proposed framework is demonstrated as a viable pathway to enable data-efficient machine learning when abundant data is available. An implementation of the method is available in a companion repository (https://github.com/NREL/Phase-space-sampling).